The decomposition method for a Hirota–Satsuma coupled KdV equation and a coupled MKdV equation

The main goal of this article is to demonstrate the use of the decomposition method that was developed by George Adomian [Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Boston, MA.] to obtain solitary wave solutions for a new Hirota–Satsuma coupled KdV equation and a coupled MKdV equation [Fan, E. G. (2001). Soliton solution for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation. Phys. Lett. A, 282, 18–22 and Wu, Y. T., Geng, X. G., Hu, X. B. and Zhu, S. M. (1999). Phys. Lett. A, 255, 259.]. The algorithm is illustrated by studying an initial value problem. The obtained results are presented, and only few terms are required to obtain an approximation solution that is found to be accurate and efficient.